Solve (7v^2-3v-2)+(6v^2-v+5)

$$( 7 v ^ { 2 } - 3 v - 2 ) + ( 6 v ^ { 2 } - v + 5 )$$

Evaluate

$$13v^{2}-4v+3$$

Solution Steps

Combine 7v^{2} and 6v^{2} to get 13v^{2}.

$$13v^{2}-3v-2-v+5$$

Combine -3v and -v to get -4v.

$$13v^{2}-4v-2+5$$

Add -2 and 5 to get 3.

$$13v^{2}-4v+3$$

Differentiate w.r.t. v

$$26v-4$$

Steps Using Derivative Rule for Sum

Combine 7v^{2} and 6v^{2} to get 13v^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(13v^{2}-3v-2-v+5)$$

Combine -3v and -v to get -4v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(13v^{2}-4v-2+5)$$

Add -2 and 5 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}v}(13v^{2}-4v+3)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 13v^{2-1}-4v^{1-1}$$

Multiply 2 times 13.

$$26v^{2-1}-4v^{1-1}$$

Subtract 1 from 2.

$$26v^{1}-4v^{1-1}$$

Subtract 1 from 1.

$$26v^{1}-4v^{0}$$

For any term t, t^{1}=t.

$$26v-4v^{0}$$

For any term t except 0, t^{0}=1.

$$26v-4$$